auth: improve ClientAuthenticator error messaging #2334

Job	Run time
checks / pre-commit	39s
checks / readme-snippets	12s
checks / test (3.10, locked, windows-latest)	2m 44s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 6s
checks / test (3.10, locked, ubuntu-latest)	59s
checks / test (3.10, lowest-direct, windows-latest)	2m 46s
checks / test (3.12, locked, ubuntu-latest)	1m 6s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 12s
checks / test (3.11, locked, ubuntu-latest)	58s
checks / test (3.13, locked, ubuntu-latest)	59s
checks / test (3.13, locked, windows-latest)	2m 34s
checks / test (3.12, lowest-direct, windows-latest)	6m 1s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 20s
checks / test (3.14, locked, ubuntu-latest)	2m 7s
checks / test (3.13, lowest-direct, windows-latest)	2m 53s
checks / test (3.13, lowest-direct, ubuntu-latest)	57s
checks / test (3.12, locked, windows-latest)	3m 34s
checks / test (3.11, locked, windows-latest)	2m 52s
checks / test (3.14, locked, windows-latest)	3m 21s
checks / test (3.14, lowest-direct, windows-latest)	2m 22s
checks / test (3.11, lowest-direct, windows-latest)	2m 38s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 3s
all-green	3s
	44m 26s

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